Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

Find the Domain of the Real Valued Function of Real Variable: (Iii) F ( X ) = √ 9 − X 2 - Mathematics

Find the domain of the real valued function of real variable:

(iii) $f\left( x \right) = \sqrt{9 - x^2}$

Solution

(iii) Given:

$f\left( x \right) = \sqrt{9 - x^2}$
We observe that f (x) is defined for all satisfying
9 -x2 ≥ 0 .
⇒ x2 -9 ≤ 0
⇒ (x + 3)(x -3) ≤ 0
⇒-3 ≤ x ≤ 3
x ∈ [ -3, 3]
Hence, domain ( f ) = [-3, 3]
Is there an error in this question or solution?

APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.3 | Q 2.3 | Page 18